High-quality x-ray absorption fine structure (XAFS) spectra of the Br-2, GeCl4, and BBr3 molecules, collected at a third generation synchrotron radiation source above the Br or Ge K-edges, are presented. Excellent fits are obtained using model spectra calculated in the muffin-tin approximation assuming Gaussian atomic distributions. The extended energy ranges of the spectra (up to 24 Angstrom(-1) for Br-2) contribute to the reduction of the statistical errors in the structural parameters. We show that the potential accuracy of present XAFS determinations is 0.001 Angstrom in bond lengths and 0.0001 Angstrom(2) in vibrational amplitudes. These results demonstrate that XAFS is nowadays competitive with electron diffraction in the determination of simple molecular structures in the presence of heavy atomic species.